Multiply the following complex numbers: $({-1+i}) \cdot ({5+2i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-1+i}) \cdot ({5+2i}) = $ $ ({-1} \cdot {5}) + ({-1} \cdot {2}i) + ({1}i \cdot {5}) + ({1}i \cdot {2}i) $ Then simplify the terms: $ (-5) + (-2i) + (5i) + (2 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -5 + (-2 + 5)i + 2i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -5 + (-2 + 5)i - 2 $ The result is simplified: $ (-5 - 2) + (3i) = -7+3i $